I think Auden is trying to say that the government lead the country into war without much thought for their people. Auden calls the war a "game" like the government is playing pieces on a board to gain the most power. While the whole country is affected by the negative factors of war, governors are continuing to play their "game". Unfortunately, citizens don't have the power to stop wars from happening.

Spiritus Mundi means world spirit in Latin. To Yeats, authors and poets have a universal muse that provides inspiration (https://study.com/academy/lesson/spiritus-mundi-definition-lesson-quiz.html). So, based on Spiritus Mundi, the image of the Sphinx in the next line is a symbol.

These 5 lines in the stanza describe the speaker's physical appearance. He says that he dresses in nice clothes, but he is afraid of people taking notice of his balding head and his thin arms and legs. This could show the speaker's insecurities. He knows he is not attractive and he tries to make up for it by wearing nice clothes. He seems to be imagining that people will notice his flaws, which is why he predicts that others will comments on his hair and thin limbs.

These two lines interested me mostly because the speaker personified the yellow fog and the yellow smoke. Even though the fog and smoke are the same, he gives them each it's own characteristic. "The yellow fog rubs its back on the window-panes", this reminds me of a cat arching its back to rub it on something to scratch its back. "The yellow smoke rubs its muzzle on the window panes", reminds me of a dog rubbing its snout against something. Also, the fog may indicate the location like an over-populated city because it produces a lot of pollution so the air is very yellow.